It used to be that Google would show Adwords only on the right side of the screen. There would be a maximum of eight ads for each page. Then, they started to show between one and three ads above the SERPs. There still are a maximum of eight ads on the right-hand side.
The question is more what makes sponsored results appear above the SERPs? Or as many call it, in the yellow boxed portion at the top and left of the screen.
There are two main conditions. Obviously you need to rank in the top three positions but you also need a minimum quality score. I believe this to be a score of seven. If your QS is below, even bidding high enough to get you to the top will not get you there.
There is not a minimum number of advertisers needed. In other words, you could have only four advertisers being served and up to three could still make it above the SERPs. Indeed, there could be only three advertisers and all three making it above the SERPs.
If no advertiser meets all the requirements, it is possible to see no ad above the SERPs. It is also possible to see only one or two. Three is currently the maximum but that could change in the future (I’ve seen Yahoo with four.)